Reconstructing prehistoric humans is an art. It's also something of a science, because the reconstructor has only fossils to work with. He or she must take those fossils, add muscles and skin, and decide exactly how they might have looked and moved. This is not easy, and sometimes the results are dictated by the popular attitudes --- usually about unrelated subjects --- of the time the reconstruction is done. This is why some early 20th century reconstructions of Neandertals are basically pretty awful.
There is still some of this, because when it comes to Neandertals, there are "difference mongers" and "similarity mongers". The "difference mongers" tend to feel that Neandertals were, indeed, very "different" from "us". Which, perhaps, in some ways, they were. But then, it's possible that early "modern" humans were also different from more recent "modern" humans. This is somewhat the position of the "similarity mongers".
As far as reconstructing what Neandertals may have actually looked like, the "similarity mongers" seem to be in the majority at this time. One example comes from a blog called Mundo Neandertal(which, unfortunately for me, is in Spanish, and my Spanish isn't that good! Still, it's an interesting picture. And it's quite recent! It's so recent that the somewhat older woman in the middle, talking to the younger woman as they cook somkething over a fire, looks a great deal like --- Hillary Clinton! And please don't ask me if that's some sort of comment on the future Secretary of State. I really don't have any idea. But this reconstruction does take into consideration that Neandertals were probably light haired, skinned, and eyed, like many Europeans today. Hence, the younger woman is definitely blond.
There's another pciture of Neandertals, that's --- in my opinion --- somewhat more "mixed". It's also from this Mundo Neandertal. I think this particular picture is supposed to conjure up images of a Neandertal Adam and Eve. The woman looks kind of like the central female character in a sort of "thriller with Neandertals" that I have on hold right now, but her eyebrows are thicker and darker than I would envision Eln's eyebrows(she has some rather unusual abilities, too). The man? Well, he's awfully hairy, and lots of people seem to think Neandertals had lots of hair(this despite evidence that they made some sort of clothing!) He's a little too "beetling", too. But they both are reccognizablyhuman. Which in my opinion, is a vast improvement over some earlier reconstructions. The makers of these reconstructions seemed to be under the impression that Neandertals were more like great apes than "late archaic" humans. I'm glad times have changed somewhat.